Let Y1, Y2, . . . , Yn denote a random sample

Chapter 9, Problem 51E

(choose chapter or problem)

Let $Y_{1}, Y_{2}, \ldots, Y_{n}$ denote a random sample from the probability density function

$f(y \mid \theta)=\left\{\begin{array}{ll}e^{-(y-\theta),} & y \geq \theta \\0, & \text { elsewhere }\end{array}\right.$

Show that $Y_{(n)}=\min \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)$ is sufficient for $\theta$.

Equation Transcription:

${Y}_{1},\ {Y}_{2},\ ....,\ {Y}_{n}$

$f\ (y\ |\ \theta{})=$ $\{{\ }_{0,\ \ \ \ \ \ \ \ \ \ \ \ elsewhere}^{{e}^{-(y-\theta{}),\ \ \ \ \ \ \ y\ \geq{}\ \theta{}}}$

${Y}_{(n)}$ = min $\left({{Y}_{1},\ {Y}_{2},\ ....,\ {Y}_{n}}\right)$

$\theta{}$

Text Transcription:

Y_1, Y_2, …., Y_n

f(y | theta) = {e^{-(y - theta),} & y geq theta 0, & \text { elsewhere }

Y_(n) = min (Y_1, Y_2, …., Y_n)

theta

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